Moore-Penrose

At this point, we can expand the Moore-Penrose right pseudoinverse:

More on Bürger et al 2006 « Climate Audit 2006

Bürger et al used Moore-Penrose pseudoinverse inverse notation, which I had not used.

More on Bürger et al 2006 « Climate Audit 2006

The error in Bürger et al equation 8 appears to be traceable to the following property of Moore-Penrose pseudoinverses.

More on Bürger et al 2006 « Climate Audit 2006

Suppose that R is a rectangular matrix and S is a square matrix, if you do a right Moore-Penrose pseudoinverse, but the following does NOT hold

More on Bürger et al 2006 « Climate Audit 2006

The Moore-Penrose pseudoinverse is familiar to people who use linear regressions:

More on Bürger et al 2006 « Climate Audit 2006

Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed.

BioMed Central - Latest articles Nicole Kramer 2009

Burger et al proposed a formula based on a Moore-Penrose inverse, but I don’t think that they’ve got the linear algebra “right” in the sense of replicating Mann.

AR1 on First Differences « Climate Audit 2006